Confidence intervals and ellipsoids for estimable functions and estimable vectors in models with orthogonal block structure

Sub-models of mixed linear models are considered. The independence of these sub-models leads to sufficient statistics for the parameters relevant for their densities. Using pivot variables, confidence regions are obtained as well hypothesis testing for variance components, estimable functions, and estimable vectors. In addition, to compare the estimators and the models, we present the histograms with the empirical joint densities for positive and negative parts of the estimators. The figures, for the two-dimensional charts, contain the corresponding UMVUE and are all unimodal with the UMVUE near the mode. The nearness of the estimators and the modes validates the presented methodology and allows the safe use of induced densities. A numerical example applied to real data is presented.     

Examining preservice teachers’ noticing of equity-based teaching practices to empower students engaging in productive struggle

Our study examined ways preservice teachers (PSTs) make connections between teaching practices and use of student resources that support productive struggle and promote equity. Our research questions are: (1) How do PSTs notice and describe the equity-based mathematics teaching practice of leveraging student resources to support student struggles? and (2) In what ways do PSTs make connections to and interpret the role student resources play in the resolution of students’ mathematical struggles? The qualitative study examined 39 PSTs in a mathematics content course for PSTs. Data come from a video analysis assignment where PSTs described their mathematical interpretations of the student struggle(s) and teacher’s use of student resources to support the struggle resolution. Findings show that PSTs noticed teacher moves that leveraged student’s mathematical thinking and linguistic funds of knowledge and based the productive level of the struggle on actions built upon peers, linguistic knowledge and prior mathematical knowledge.     

Simulation of the interaction of light with 3-D metallic nanostructures using a proper orthogonal decomposition-Galerkin reduced-order discontinuous Galerkin time-domain method

In this artice, we report on a reduced-order model (ROM) based on the proper orthogonal decomposition (POD) technique for the system of 3-D time-domain Maxwell's equations coupled to a Drude dispersion model, which is employed to describe the interaction of light with nanometer scale metallic structures. By using the singular value decomposition (SVD) method, the POD basis vectors are extracted offline from the snapshots produced by a high order discontinuous Galerkin time-domain (DGTD) solver. With a Galerkin projection and a second order leap-frog (LF₂) time discretization, a discrete ROM is constructed. The stability condition of the ROM is then analyzed. In particular, when the boundary is a perfect electric conductor condition, the global energy of the ROM is bounded, which is consistent with the characteristics of global energy in the DGTD method. It is shown that the ROM based on Galerkin projection can maintain the stability characteristics of the original high dimensional model. Numerical experiments are presented to verify the accuracy, demonstrate the capabilities of the POD-based ROM and assess its efficiency for 3-D nanophotonic problems.     

A flexible block classical Gram–Schmidt skeleton with reorthogonalization

We investigate a variant of the reorthogonalized block classical Gram–Schmidt method for computing the QR factorization of a full column rank matrix. Our aim is to bound the loss of orthogonality even when the first local QR algorithm is only conditionally stable. In particular, this allows the use of modified Gram–Schmidt instead of Householder transformations as the first local QR algorithm. Numerical experiments confirm the stable behavior of the new variant. We also examine the use of non-QR local factorization and show by example that the resulting variants, although less stable, may also be applied to ill-conditioned problems.     

Convergence to a terrace solution in multistable reaction–diffusion equation with discontinuities

In this paper we address the large-time behavior of solutions of bistable and multistable reaction–diffusion equation with discontinuities around the stable steady states. We show that the solution always converges to a special solution, which may either be a traveling wave in the bistable case, or more generally a terrace (i.e. a collection of stacked traveling waves with ordered speeds) in the multistable case.     

带有相依重尾冲击的Poisson噪音过程尾的一致渐近性质

本文考虑了带有某种相依重尾冲击的Poisson噪音过程尾的一致渐近性质.当冲击是二元上尾渐近独立的非负随机变量具有长尾和控制变化尾分布且噪音函数具有正的上下界时,得到了过程尾概率的一致渐近公式.进而,当冲击具有连续的一致变化尾分布时,去除了噪音函数具有正的下界的限制.对于噪音函数不一定具有正的上界的情形,当冲击具有两两负象限相依结构时,也得到了一致渐近性结果.     

Efficient Synthesis of Submicrometer-Sized Active Pharmaceuticals by Laser Fragmentation in a Liquid-Jet Passage Reactor with Minimum Degradation

One challenge in the development of new drug formulations is overcoming their low solubility in relevant aqueous media. Reducing the particle size of drug powders to a few hundred nanometers is a well-known method that leads to an increase in solubility due to an elevated total surface area. However, state-of-the-art comminution techniques like cryo-milling suffer from degradation and contamination of the drugs, particularly when sub-micrometer diameters are aspired that require long processing times. In this work, picosecond-pulsed laser fragmentation in liquids (LFL) of dispersed drug particles in a liquid-jet passage reactor is used as a wear-free comminution technique using the hydrophobic oral model drugs naproxen, prednisolone, ketoconazole, and megestrol acetate. Particle size and morphology of the drug particles are characterized using scanning electron microscopy (SEM) and changes in particle size distributions upon irradiation are quantified using an analytical centrifuge. The findings highlight the superior fragmentation efficiency of the liquid-jet passage reactor setup, with a 100 times higher fraction of submicrometer particles (SMP) of the drugs compared to the batch control, which enhances solubility and goes along with minimal chemical degradation (<1%), determined by attenuated total reflection-Fourier transform infrared spectroscopy (ATR-FTIR), high-performance liquid chromatography (HPLC), and X-ray diffraction (XRD). Moreover, the underlying predominantly photo-mechanically induced laser fragmentation mechanisms of organic microparticles (MP) are discussed.     

超声全矩阵数据联合稀疏重构的多测量向量模型应用

针对单测量向量模型(Single Measurement Vector,SMV)等传统压缩感知方法处理超声全矩阵数据时,存在重构精度低和重构耗时长等问题,本文研究了多测量向量模型(Multiple Measurement Vectors,MMV)应用的可行性。针对铝合金试块中不同深度的φ2 mm横通孔,分别使用MMV模型中的多测量稀疏贝叶斯(Multiple Sparse Bayesian Learning,MSBL)算法和SMV模型中的稀疏贝叶斯(Sparse Bayesian Learning,SBL)算法进行超声全矩阵数据重构,并实施全聚焦成像。随后,引入归一化均方误差和阵列性能因子评价图像和信号的重构效果。实验结果表明,SBL算法在25%采样率时的归一化均方误差为1.9%,而MSBL算法仅需15%采样率即可达到相似效果且耗时更少。     

Highly Strong Interaction between Fe/Fe3C Nanoparticles and N-Doped Carbon toward Enhanced Oxygen Reduction Reaction Performance

Transition metal compounds anchored on N-doped carbon (NC) show intrinsic activity and stability for oxygen reduction reaction (ORR). However, the interaction between the transition metal compounds and NC still needs to be strengthened for electron transfer at the compounds/carbon interface. Herein, Fe/Fe₃C hybrid nanoparticles encapsulated into N-doped carbon (Fe@NC) are used as high-performance ORR catalysts. Benefiting from the strong interaction at Fe/Fe₃C nanoparticles/NC interface, the electrons can transfer from Fe/Fe₃C hybrid nanoparticles to NC, redistributing the electron density of active sites and promoting the ORR process. The as-synthesized Fe@NC exhibits outstanding ORR catalytic activity with an onset potential of 1.01 V and a half-wave potential of 0.92 V in alkaline media. It also shows prominent cycling stability and tolerance to methanol crossover, superior to Pt/C catalyst. The theoretical analysis reveals that the Fe nanoparticles have regulated the electron distributions at the heterojunction interface. The Gibbs free energy diagrams for ORR illustrate that the rate-determining step is the conversion of OH* to OH⁻. In situ Raman spectra give evidence of O-containing intermediates to prove the ORR process.     

Effect of plasma-activated water and buffer solution combined with ultrasound on fungicide degradation and quality of cherry tomato during storage

The purpose of this study was to examine plasma-activated buffer solution (PABS) and plasma-activated water (PAW) combined with ultrasonication (U) treatment on the reduction of chlorothalonil fungicide and the quality of tomato fruits during storage. To obtain PAW and PABS, an atmospheric air plasma jet was used to treat buffer solution and deionized water at different treatment times (5 and 10 min). For combined treatments, fruits were submerged in PAW and PABS, then sonicated for 15 min, and individual treatment without sonication. As per the results, the maximum chlorothalonil reduction of 89.29% was detected in PAW-U₁₀, followed by 85.43% in PABS. At the end of the storage period, the maximum reduction of 97.25% was recorded in PAW-U₁₀, followed by 93.14% in PABS-U₁₀. PAW, PABS, and both combined with ultrasound did not significantly affect the overall tomato fruit quality in the storage period. Our results revealed that PAW combined with sonication had a significant impact on post-harvest agrochemical degradation and retention of tomato quality than PABS. Conclusively, the integrated hurdle technologies effectively reduce agrochemical residues, which helps to lower health hazards and foodborne illnesses.